The z-pinch is a well known physical phenomenon. It is the basis for one of the simplest devices for containing and compressing a plasma, or gaseous mixture of electrons and ions. It has been extensively investigated in the quest for controlled nuclear fusion and as a source of x-rays and other forms of electromagnetic radiation. See for example L. A. Artsimovich, Controlled Thermonuclear Reactions (Gordon and Breach, New York, 1964), Chap. 5, Fast High Power Discharges; N. A. Krall and A. W. Trivelpiece, Principles of plasma physics (McGraw-Hill, New York, 1973), Chap. 3, p. 100-126; and M. A. Lieberman, J. S. De Groot, A. Toor, and R. B. Spielman, Physics of high-density Z-pinch plasmas (Springer-Verlag, New York, 1999), Chap. 7, Applications of Z Pinches, p. 236.
Briefly, when a gas is excited above a particular energy level a portion of the gas becomes ionized to form a plasma, which consists of a mixture of free electrons, gaseous ions, and gaseous atomic or molecular species remaining unionized. Gases can be ionized to form a plasma in various ways, including for example by the application of an electrical discharge, a laser beam, or microwave radiation. A recent example of plasma production by laser induced ionization of a gas is reported by Ackermann et al., Appl. Physics Letters, Vol. 85, No. 23, p. 5781 (2004).
When a high power electrical pulse is applied to a plasma column contained in a cylindrical tube, so as to create a rapidly increasing and large electrical current flowing through the plasma, there is generated a magnetic field which has azimuthal or cylindrical symmetry, with circular field lines centered on the axis of the plasma column. The rapidly increasing magnetic field confines and compresses the plasma radially inwardly toward the axis, thereby heating the plasma. This is known as z-pinch compression. The rising current driven axially through the plasma column produces an increasing azimuthally symmetric magnetic field and the pinching phenomenon of the column (z-pinch) takes place due to the magnetic pressure created by the interaction of the magnetic field and the current itself. This compression must take place in a sufficiently short time that the plasma cannot exchange heat with the surrounding gas. With a sufficiently high rate of increase in the current, the plasma is compressed essentially adiabatically and the work expended during by the radial magnetic compression is transformed into heat. Confinement, compression, and heating all occur essentially simultaneously.
Because both a high current and a high rate of increase in the current are needed, as a practical matter z-pinch compression can be achieved only in short bursts, driven by high voltage, high power electrical pulses. The extent of magnetic compression is effectively limited by the availability of suitable power supplies. In order to achieve the high power pulses needed for this purpose, capacitor-based and induction-based power supplies and the like have typically been used for z-pinch devices. Nevertheless, it is possible to obtain a balance between the radially outward pressure of the plasma and the radially inward magnetic compression on a time scale shorter than the time scale of the diffusion of the magnetic field into the plasma.
Despite the simplicity of this explanation, the actual physical phenomena are very complex, as the response of the z-pinch plasma leads to nonlinear hydrodynamic phenomena that result in detrimental instabilities, as well as multiple atomic processes including ionization, recombination, excitation, and radiation.
A soft x-ray laser based on z-pinch compression of a plasma has been previously reported, but only with non-rotating capillary tubes of limited length. See J. J. Rocca, V. Shlyaptsev, F. G. Tomasel, O. D. Cortazar, D. Hartshorn, and J. L. A. Chilla, Phys. Rev. Lett. 73, 2192 (1994), hereby incorporated by reference. To the best of our knowledge, and until present, capillary channels having lengths up to only approximately 45 cm have been used. See G. Tomasetti, A. Ritucci, A. Reale, L. Reale, L. Palladino, A. Faenov, T. Pikuz, F. Flora, L. Mezi, G. Baldacchini, R. M. Montereali, F. Bonfigli, L. Arrizza, S. V. Kukhlevsky, and J. Kaiser, Proceedings of SPIE Vol. 5197 Soft X-Ray Lasers and Applications V, San Diego, Calif., 127, (2003), edited by E. E. Feed and S. Suckewer, SPIE, Bellingham, 2003.
The previously known non-rotating capillary discharge x-ray laser involves a sequence of operations and phenomena. First, the gas in the tube must ordinarily be pre-ionized to form a cold plasma column. Pre-ionization plays a key role in achieving plasma column stability during the subsequent z-pinch.
Small diameter capillary tubes have been seen as desirable for such lasers because they were considered to require less electrical power to achieve sufficient z-pinch compression to result in generation of coherent x-rays. However, upon formation of the initial cold plasma by appropriate excitation of the gas in a capillary tube, some quantity of the capillary wall material is unavoidably ablated. This results in impurity atoms being ionized and introduced into the plasma, having a detrimental effect on the necessary parameters of the lasing plasma. Wall ablation in capillary discharges is unfavorable both for the compression and the stability of the plasma, and consequently has a detrimental effect on soft x-ray laser production. Further, the quantity of ablated material increases with the surface area of the capillary wall, which in turn increases with the length of the capillary. Consequently, since the laser radiation must pass through the entire length of the plasma column, the capillary length cannot be increased beyond several tens of centimeters, due to the requirements of high uniformity and stability as well as minimal quantity of material ablated from the wall during plasma formation. Accordingly, avoiding ablation is an important objective.
Capillary tubes have also been used because close proximity of the capillary wall to the plasma column has the advantage of suppressing instabilities in the z-pinch plasma. However, another disadvantage, in addition to the degradation of the plasma by contamination with ablated material, is that changing the initial composition of the ionized gas mixture through material ablation increases the cooling of the plasma through thermal conduction.
High-pressure plasma columns formed inside a rotating tube have been suggested as sources of non-coherent infrared, visible, ultraviolet and x-ray radiation. U.S. Pat. No. 6,417,625 to Brooks, for example, discloses the use of a rotating tube containing a feed gas at atmospheric pressure to achieve “vortex stabilization” for the purpose of stabilizing and containing an axially centered plasma column that is formed by any one of various processes, including formation by electrical discharge, microwave excitation or radio frequency excitation. The rotating tube creates an annular sheath of relatively cooler gas that functions to thermally and electrically isolate the high temperature plasma column from the inside wall of the rotating tube. There is obtained a stable, steady state plasma that continuously emits non-coherent radiation at wavelengths that are determined by the temperature of the plasma and the gaseous ionic species the plasma.
Stimulated emission of radiation from a plasma medium, or laser radiation, requires a population inversion of energy levels among the ionic and molecular species constituting the plasma, which exists whenever more atoms or ions are excited to an upper energy level than remain in a lower energy level. In this regard, the energy of a photon emitted in a radiative transition caused by decay of an electron from an excited energy level to a lower energy level of an ionic species is directly proportional to the energy difference between the upper and lower energy levels, and consequently a short-wavelength laser must have a large energy gap. However, the rate at which electrons in the upper energy level decay by the spontaneous decay, which defeats the creation of the population inversion necessary to achieve stimulated emission, increases extremely rapidly as the energy gap increases. Consequently, to achieve stimulated emission of radiation in the soft x-ray wavelength range not only is more energy necessary to raise atoms or ions from their ground state to the upper energy levels, but they must also be excited, or pumped, at a faster rate. Consequently the required pump power dramatically increases as higher energy radiation is sought. For efficient energy extraction of coherent radiation from a lasing medium such as a plasma, with its highly charged ions as radiation emitters, it is necessary to operate in the regime of gain saturation. This means to maintain the maximum possible population inversion by pumping the lasing medium so that the stimulated emission of radiation takes place over the longest obtainable optical path. In transient schemes, in which electrical current is increased rapidly, the population inversion in the plasma has a short life and the duration of the gain is much shorter than in optical lasers. Therefore, the stimulated emission and accompanying radiation amplification of soft x-ray radiation in a plasma takes place in a single or a double-pass through the lasing plasma medium. Consequently the plasma length plays a key role because the spectrally integrated intensity increases approximately exponentially with the plasma length according to Linford's formula. However, it is actually the length-to-diameter aspect ratio of the elongated plasma column, together with its very high uniformity, which are the crucial parameters for its quality as a lasing medium. The radiation traveling through the plasma column also experiences refraction produced by the spatial variation, particularly in the radial direction, of the electron density radial profile. Plasma columns having a density minimum on axis, or a concave radial profile of the electron density, have been achieved, primarily by rotation, as disclosed for example in Brooks.
Accordingly, it is an object and purpose of the present invention to provide an improved method and apparatus for producing soft x-ray laser radiation by z-pinch compression of a gaseous plasma.
It is also an object and purpose to provide a soft x-ray laser that is based on z-pinch compression of a rotating plasma and which is thereby characterized by reduced ablation of material from the walls of the plasma containment vessel.
It is yet another object and purpose to provide an improved method of producing soft x-ray laser radiation utilizing z-pinch compression of a low pressure gaseous plasma that is driven in rotation magnetically as well as mechanically.
It is a further object to provide a soft x-ray laser based on z-pinch compression of a plasma column, in which the density profile of the column results in reduced refraction losses of the laser radiation while also minimizing ablation of the containment vessel.